%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : CAT038^1 : TPTP v6.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n089.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:19:55 EDT 2014

% Result   : Timeout 300.00s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : CAT038^1 : TPTP v6.1.0. Released v4.1.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:12:06 CDT 2014
% % CPUTime  : 300.00 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x18a78c0>, <kernel.Constant object at 0x18a7488>) of role type named a
% Using role type
% Declaring a:fofType
% FOF formula (<kernel.Constant object at 0x1b2a248>, <kernel.Single object at 0x18a74d0>) of role type named b
% Using role type
% Declaring b:fofType
% FOF formula ((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) of role conjecture named swap
% Conjecture to prove = ((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))):Prop
% We need to prove ['((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))']
% Parameter fofType:Type.
% Parameter a:fofType.
% Parameter b:fofType.
% Trying to prove ((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found eta_expansion000:=(eta_expansion00 (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) (fun (x:(fofType->fofType))=> ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a))))
% Found (eta_expansion00 (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b0)
% Found ((eta_expansion0 Prop) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b0)
% Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b0)
% Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b0)
% Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b0)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a)))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x a)) b)) (((eq fofType) (x b)) a))))
% Found x01:(P (x b))
% Found (fun (x01:(P (x b)))=> x01) as proof of (P (x b))
% Found (fun (x01:(P (x b)))=> x01) as proof of (P0 (x b))
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->fofType)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->fofType)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->fofType)->Prop)) a0) as proof of (((eq ((fofType->fofType)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->fofType)->Prop)) a0) as proof of (((eq ((fofType->fofType)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->fofType)->Prop)) a0) as proof of (((eq ((fofType->fofType)->Prop)) a0) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq ((fofType->fofType)->Prop)) b0) (fun (x:(fofType->fofType))=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found eq_ref00:=(eq_ref0 (((eq fofType) (x b)) a)):(((eq Prop) (((eq fofType) (x b)) a)) (((eq fofType) (x b)) a))
% Found (eq_ref0 (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found ((eq_ref Prop) (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found ((eq_ref Prop) (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found ((eq_ref Prop) (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found x01:(P (x b))
% Found (fun (x01:(P (x b)))=> x01) as proof of (P (x b))
% Found (fun (x01:(P (x b)))=> x01) as proof of (P0 (x b))
% Found x0:(P (x b))
% Instantiate: b0:=(x b):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (x b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (x b)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found x0:(P a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x02:(P (x b))
% Found (fun (x02:(P (x b)))=> x02) as proof of (P (x b))
% Found (fun (x02:(P (x b)))=> x02) as proof of (P0 (x b))
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found x02:(P a)
% Found (fun (x02:(P a))=> x02) as proof of (P a)
% Found (fun (x02:(P a))=> x02) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b0:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b0
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((conj00 ((eq_ref fofType) (x a))) eq_sym0) as proof of ((and (((eq fofType) (x a)) b)) b0)
% Found (((conj0 b0) ((eq_ref fofType) (x a))) eq_sym0) as proof of ((and (((eq fofType) (x a)) b)) b0)
% Found ((((conj (((eq fofType) (x a)) b)) b0) ((eq_ref fofType) (x a))) eq_sym0) as proof of ((and (((eq fofType) (x a)) b)) b0)
% Found ((((conj (((eq fofType) (x a)) b)) b0) ((eq_ref fofType) (x a))) eq_sym0) as proof of ((and (((eq fofType) (x a)) b)) b0)
% Found ((((conj (((eq fofType) (x a)) b)) b0) ((eq_ref fofType) (x a))) eq_sym0) as proof of (P b0)
% Found x0:(P (x b))
% Instantiate: b0:=(x b):fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P0 b0)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 (x b))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 (x b)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% Found x0:(P a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x02:(P (x b))
% Found (fun (x02:(P (x b)))=> x02) as proof of (P (x b))
% Found (fun (x02:(P (x b)))=> x02) as proof of (P0 (x b))
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found x0:(P a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x02:(P a)
% Found (fun (x02:(P a))=> x02) as proof of (P a)
% Found (fun (x02:(P a))=> x02) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found x02:(P a)
% Found (fun (x02:(P a))=> x02) as proof of (P a)
% Found (fun (x02:(P a))=> x02) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq fofType) (x b)) a))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq fofType) (x b)) a))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq fofType) (x b)) a))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq fofType) (x b)) a))
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->fofType)->Prop)) b0) (fun (x:(fofType->fofType))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->fofType)) Prop) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->fofType)) Prop) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->fofType)) Prop) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found x0:(P (x b))
% Instantiate: a0:=(x b):fofType
% Found x0 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 (x b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 (x b)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 (x b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 (x b)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x10:(P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P2 a)
% Found x0:(P a)
% Instantiate: a0:=a:fofType
% Found x0 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found x0:(P b0)
% Found x0 as proof of (P0 (x b))
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found x02:(P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x02:(P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found x01:(P0 b0)
% Found (fun (x01:(P0 b0))=> x01) as proof of (P0 b0)
% Found (fun (x01:(P0 b0))=> x01) as proof of (P1 b0)
% Found x00:(P b00)
% Found (fun (x00:(P b00))=> x00) as proof of (P b00)
% Found (fun (x00:(P b00))=> x00) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x0:(P a)
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=a:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b0)
% Instantiate: b1:=b0:fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b1)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b1))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found x0:(P0 (x b))
% Found (fun (x0:(P0 (x b)))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (x b)))=> x0) as proof of ((P0 (x b))->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (x b)))=> x0) as proof of (P (x b))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found x0:(P a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x02:(P a)
% Found (fun (x02:(P a))=> x02) as proof of (P a)
% Found (fun (x02:(P a))=> x02) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found x00:(P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P0 a)
% Found (fun (x0:(P0 a))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of ((P0 a)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: a0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of a0
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((conj00 ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found (((conj0 a0) ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found ((((conj (((eq fofType) (x a)) b)) a0) ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found ((((conj (((eq fofType) (x a)) b)) a0) ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found ((((conj (((eq fofType) (x a)) b)) a0) ((eq_ref fofType) (x a))) iff_sym) as proof of (P a0)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq ((fofType->fofType)->Prop)) b0) (fun (x:(fofType->fofType))=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b0) as proof of (((eq ((fofType->fofType)->Prop)) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found x0:(P (x b))
% Instantiate: a0:=(x b):fofType
% Found x0 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->fofType))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 (x b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 (x b)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P2 b0)
% Instantiate: b0:=b:fofType
% Found (fun (x0:(P2 b0))=> x0) as proof of (P2 (x b))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 (x b)))
% Found (fun (P2:(fofType->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x10:(P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P2 a)
% Found x0:(P a)
% Instantiate: a0:=a:fofType
% Found x0 as proof of (P0 a0)
% Found x0:(P a)
% Instantiate: a0:=a:fofType
% Found x0 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found x0:(P b0)
% Found x0 as proof of (P0 (x b))
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x02:(P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x02:(P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x02:(P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x02:(P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P1 a)
% Found (fun (x02:(P1 a))=> x02) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x10:(P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x01:(P0 b0)
% Found (fun (x01:(P0 b0))=> x01) as proof of (P0 b0)
% Found (fun (x01:(P0 b0))=> x01) as proof of (P1 b0)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found x00:(P b00)
% Found (fun (x00:(P b00))=> x00) as proof of (P b00)
% Found (fun (x00:(P b00))=> x00) as proof of (P0 b00)
% Found x00:(P b00)
% Found (fun (x00:(P b00))=> x00) as proof of (P b00)
% Found (fun (x00:(P b00))=> x00) as proof of (P0 b00)
% Found x01:(P0 b0)
% Found (fun (x01:(P0 b0))=> x01) as proof of (P0 b0)
% Found (fun (x01:(P0 b0))=> x01) as proof of (P1 b0)
% Found x0:(P a)
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x0:(P a)
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=a:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=a:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b0)
% Instantiate: b1:=b0:fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b1)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b1))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b0)
% Instantiate: b1:=b0:fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b1)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b1))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a))))
% Found (eq_ref0 (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b00)
% Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b00)
% Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b00)
% Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> ((and (((eq fofType) (F a)) b)) (((eq fofType) (F b)) a)))) b00)
% Found x0:(P b0)
% Found x0 as proof of (P0 (x b))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found x0:(P0 (x b))
% Found (fun (x0:(P0 (x b)))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (x b)))=> x0) as proof of ((P0 (x b))->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (x b)))=> x0) as proof of (P (x b))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found x0:(P0 (x b))
% Found (fun (x0:(P0 (x b)))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (x b)))=> x0) as proof of ((P0 (x b))->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (x b)))=> x0) as proof of (P (x b))
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P a)
% Instantiate: b1:=a:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) (x b))
% Found x01:(P b00)
% Found (fun (x01:(P b00))=> x01) as proof of (P b00)
% Found (fun (x01:(P b00))=> x01) as proof of (P0 b00)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x01:(P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P1 b0)
% Found (fun (x01:(P1 b0))=> x01) as proof of (P2 b0)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found x00:(P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x00:(P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P0 b1)
% Found x00:(P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P0 b1)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P0 a)
% Found (fun (x0:(P0 a))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of ((P0 a)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P0 a)
% Found (fun (x0:(P0 a))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of ((P0 a)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=a:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b0)
% Instantiate: b1:=b0:fofType
% Found (fun (x0:(P0 b0))=> x0) as proof of (P0 b1)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 b1))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b0))=> x0) as proof of (P b1)
% Found x0:(P a)
% Found x0 as proof of (P0 a)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b0
% Found iff_sym as proof of a0
% Found ((conj00 ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found (((conj0 a0) ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found ((((conj (((eq fofType) (x a)) b)) a0) ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found ((((conj (((eq fofType) (x a)) b)) a0) ((eq_ref fofType) (x a))) iff_sym) as proof of ((and (((eq fofType) (x a)) b)) a0)
% Found ((((conj (((eq fofType) (x a)) b)) a0) ((eq_ref fofType) (x a))) iff_sym) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b10)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b0)
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b01)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x00:(P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P0 b1)
% Found x00:(P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P b1)
% Found (fun (x00:(P b1))=> x00) as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x0:(P0 a)
% Found (fun (x0:(P0 a))=> x0) as proof of (P0 a)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of ((P0 a)->(P0 a))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 a))=> x0) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x00:(P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (x b)) a)):(((eq Prop) (((eq fofType) (x b)) a)) (((eq fofType) (x b)) a))
% Found (eq_ref0 (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found ((eq_ref Prop) (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found ((eq_ref Prop) (((eq fofType) (x b)) a)) as proof of (((eq Prop) (((eq fofType) (x b)) a)) b0)
% Found (eq_sym0001 ((eq_ref Prop) (((eq fofType) (x b)) a))) as proof of ((P0 (x b))->(P0 a))
% Found (eq_sym0001 ((eq_ref Prop) (((eq fofType) (x b)) a))) as proof of ((P0 (x b))->(P0 a))
% Found ((fun (x0:(((eq Prop) (((eq fofType) (x b)) a)) b0))=> ((eq_sym000 x0) (fun (x1:Prop)=> (P0 (x b))))) ((eq_ref Prop) (((eq fofType) (x b)) a))) as proof of ((P0 (x b))->(P0 a))
% Found ((fun (x0:(((eq Prop) (((eq fofType) (x b)) a)) b0))=> ((eq_sym000 x0) (fun (x1:Prop)=> (P0 (x b))))) ((eq_ref Prop) (((eq fofType) (x b)) a))) as proof of ((P0 (x b))->(P0 a))
% Found (fun (P0:(fofType->Prop))=> ((fun (x0:(((eq Prop) (((eq fofType) (x b)) a)) b0))=> ((eq_sym000 x0) (fun (x1:Prop)=> (P0 (x b))))) ((eq_ref Prop) (((eq fofType) (x b)) a)))) as proof of ((P0 (x b))->(P0 a))
% Found (fun (P0:(fofType->Prop))=> ((fun (x0:(((eq Prop) (((eq fofType) (x b)) a)) b0))=> ((eq_sym000 x0) (fun (x1:Prop)=> (P0 (x b))))) ((eq_ref Prop) (((eq fofType) (x b)) a)))) as proof of (forall (P:(fofType->Prop)), ((P (x b))->(P a)))
% Found (fun (P0:(fofType->Prop))=> ((fun (x0:(((eq Prop) (((eq fofType) (x b)) a)) b0))=> ((eq_sym000 x0) (fun (x1:Prop)=> (P0 (x b))))) ((eq_ref Prop) (((eq fofType) (x b)) a)))) as proof of b0
% Found x00:(P a)
% Found (fun (x00:(P a))=> x00) as proof of (P a)
% Found (fun (x00:(P a))=> x00) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x1:(P2 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x1:(P2 b1))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b1))=> x1) as proof of ((P2 b1)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b1))=> x1) as proof of (P1 b1)
% Found x1:(P1 a)
% Instantiate: b1:=a:fofType
% Found x1 as proof of (P2 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:(P b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P a)
% Instantiate: a0:=a:fofType
% Found x0 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b00)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b00)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b00)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x0:(P1 b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P2 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P1 b0)
% Instantiate: b1:=b0:fofType
% Found x0 as proof of (P2 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x01:(P0 (x b))
% Found (fun (x01:(P0 (x b)))=> x01) as proof of (P0 (x b))
% Found (fun (x01:(P0 (x b)))=> x01) as proof of (P1 (x b))
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found x00:(P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P1 b0)
% Found (fun (x00:(P1 b0))=> x00) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x0:(P1 a)
% Instantiate: b0:=a:fofType
% Found x0 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found x1:(P1 b0)
% Instantiate: b1:=b0:fofType
% Found x1 as proof of (P2 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P1 a)
% Instantiate: a0:=a:fofType
% Found x0 as proof of (P2 a0)
% Found x0:(P1 a)
% Instantiate: a0:=a:fofType
% Found x0 as proof of (P2 a0)
% Found x0:(P b0)
% Instantiate: a0:=b0:fofType
% Found x0 as proof of (P0 a0)
% Found x01:(P0 (x a))
% Found (fun (x01:(P0 (x a)))=> x01) as proof of (P0 (x a))
% Found (fun (x01:(P0 (x a)))=> x01) as proof of (P1 (x a))
% Found x01:(P0 (x b))
% Found (fun (x01:(P0 (x b)))=> x01) as proof of (P0 (x b))
% Found (fun (x01:(P0 (x b)))=> x01) as proof of (P1 (x b))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b00)
% Found x1:(P2 b00)
% Instantiate: b00:=a:fofType
% Found (fun (x1:(P2 b00))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b00))=> x1) as proof of ((P2 b00)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b00))=> x1) as proof of (P1 b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x1:(P2 b1)
% Instantiate: b1:=a:fofType
% Found (fun (x1:(P2 b1))=> x1) as proof of (P2 a)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b1))=> x1) as proof of ((P2 b1)->(P2 a))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b1))=> x1) as proof of (P1 b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x1:(P2 b0)
% Instantiate: b1:=b0:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b1)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b1))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (x b))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x0:(P0 b1)
% Instantiate: b1:=b:fofType
% Found (fun (x0:(P0 b1))=> x0) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 b1))=> x0) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b1)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b1)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b1)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b1)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b1)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b1)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b1)
% Found eq_ref00:=(eq_ref0 (x b)):(((eq fofType) (x b)) (x b))
% Found (eq_ref0 (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found ((eq_ref fofType) (x b)) as proof of (((eq fofType) (x b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 (x a)):(((eq fofType) (x a)) (x a))
% Found (eq_ref0 (x a)) as proof of (((eq fofType) (x a)) b0)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b0)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b0)
% Found ((eq_ref fofType) (x a)) as proof of (((eq fofType) (x a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x10:(P1 a0)
% Found (fun (x10:(P1 a0))=> x10) 
% EOF
%------------------------------------------------------------------------------